Labor has accused the Australian government of breaching privacy laws by leaking confidential information about Centrelink customers.

The accusation stems from Centrelink's new automated debt recovery system that has seen some letters demanding money repayment sent in error to welfare recipients.

Opposition human services spokeswoman Linda Burney moved a motion in the lower house on Tuesday, arguing that the government had conducted a vindictive campaign to gag those who complain about the Centrelink scandal by leaking their details to the media.

"They have made it clear: If you speak out, they will target you," she said. "They wanted revenge on those who have spoken publicly. We serve the people in this place, and it's not for us to target them."

Burney is also demanding an apology on behalf of those she said have been targeted, while the rest of her party is demanding the government reveal who authorised the release of the confidential information.

The remarks came after it was revealed the Department of Human Services (DHS) provided information on welfare recipient Andie Fox following an article she wrote for Fairfax Media.

In the article written earlier this month, Fox detailed the difficulties she had in dealing with the agency after she began receiving calls from a debt collector.

Fairfax Media published another article over the weekend that cited information provided by Centrelink, including details of Fox's interactions with Centrelink and her claims history.

Minister for Human Services Alan Tudge insisted that the government is allowed to release a person's private information under social services laws in order to correct the record.

"In cases where people have gone to the media with statements that are incorrect or misleading ... we are able to release information about the person for the purposes of correcting a mistake," he told Parliament on Tuesday.

"It allows the correction of false information which has been placed into the media."

During Senate Estimates on Tuesday, Australian Information and Privacy Commissioner Timothy Pilgrim requested that DHS consider the sensitivity of the information it holds, and said he would be looking into the release of personal information from within the department, but stressed that he was not opening a formal investigation at this stage.

Pilgrim did say, however, that there are particular circumstances where laws that govern the operation of a government organisation are able to override those present in the Privacy Act.

As the Centrelink debt recovery fiasco was unfolding in early January, Pilgrim said his office had been in contact with DHS, as well as the Office of the Commonwealth Ombudsman; however, no investigation into the matter was opened as a result.

"My office works closely with DHS and other government agencies to ensure they understand their privacy obligations and adopt best practice when undertaking data-matching activities," Pilgrim said at the time.

"We also undertake assessments (formerly termed audits) of DHS' data-matching activities to ensure that the personal information collected through these processes continues to be managed in accordance with the Privacy Act 1988."

In February, the Senate passed a motion to initiate an inquiry into the "robo-debt" system that will be chaired by Greens Senator Rachel Siewert.

The new system automatically compares the income people declare to the Australian Taxation Office against income declared to Centrelink. When it detects a disparity, Centrelink automatically issues a debt notice and that debt comes with a 10 percent recovery fee.

One large error in the Centrelink system is that it was incorrectly calculating a recipient's income, basing a recipient's fortnightly pay on their annual salary rather than taking a cumulative 26-week snapshot of what an individual was paid.

Previously, Community and Public Sector Union (CPSU) national secretary Nadine Flood said she was looking forward to the Senate inquiry in order to shine a light on what has caused the "shameful robo-debt crisis".

"The Department of Human Services has been far more concerned with gagging its staff and fudging its performance indicators than fixing this mess, so this is an important opportunity for staff to speak openly about how things have gone so wrong and their suggestions to maintain the integrity of our welfare system without the unnecessary collateral damage," Flood said.

"Our members were warning for months that this automated debt system would not work, but this is an agency where the bosses don't listen to their staff. The situation has highlighted the dysfunctional workplace culture across this agency, and the damage caused by years of budget cuts and the 5,000 jobs that have been slashed."

Prime Minister Malcolm Turnbull previously called the debt recovery system "quite appropriate" and said it boils down to the fact that the government has an obligation to ensure that Australia's "very extensive and generous" social welfare system is allocated correctly.

Tudge said on Tuesday the government would continue with the controversial debt recovery system in order to protect taxpayers' money.

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